We clarify the properties of the behavior of classical cosmological perturbations when the Universe experiences a bounce. This is done in the simplest possible case for which gravity is described by general relativity and the matter content has a single component, namely a scalar field in a closed geometry. We show in particular that the spectrum of scalar perturbations can be affected by the b...

Garsia and Haiman (J. Algebraic. Combin. 5 (1996), 191 − 244) conjectured that a certain sum Cn(q, t) of rational functions in q, t reduces to a polynomial in q, t with nonnegative integral coefficients. Haglund later discovered (Adv. Math., in press), and with Garsia proved (Proc. Nat. Acad. Sci. 98 (2001), 4313 − 4316) the refined conjecture Cn(q, t) = ∑ qareatbounce. Here the sum is over all...

By studying some bouncing universe models dominated by a specific class of hydrodynamical fluids, we show that the primordial cosmological perturbations may propagate smoothly through a general relativistic bounce. We also find that the purely adiabatic modes, although almost always fruitfully investigated in all other contexts in cosmology, are meaningless in the bounce or null energy conditio...

For gas spheres with masses of 104M0'"'-'1020Me, the hydro dynamical evolution, beginning from a state where the objects have become opaque, is calculated by means of an electronic computer. The effects of general relativity is included, but energy transport is neglected. The mechanism of bounce, crush and collapse is discussed qualitatively. It is shown that gas spheres with mass greater than ...

We use the polygon representation of 2+1–dimensional gravity to explicitly carry out the canonical quantization of a universe with the topology of a torus. The mapping-classinvariant wave function for a quantum ”big bounce”, is reminiscent of the interference patterns of linear gratings. We consider the “problem of time” of quantum gravity: for one choice of internal time the universe recovers ...